Distribution of the cVBS order parameter defined in Eq. (3b) for L = 32 systems with h = 0 at g = 0.80 in (a) and g = 0.78 in (b). In these calculations β=4L . The horizontal and vertical axes correspond to Re {m_c} and Im {m_c}, respectively. The color scale corresponds to a linear mapping from 0 to maximal probability density in each of the panels. The deviations from perfect Z4 symmetry in both (a) and (b) are due to slow migration of the VBS angle ϕ in the simulations.